This invention relates to solar energy receivers utilized with focused solar energy and, more particularly, to a method and apparatus for optimizing the performance of the receiver and extending its useful life.
Solar energy receivers which utilize focused solar radiation transfer the energy in the focused solar radiation to a working fluid, normally air, through the use of a heat exchanger located in the receiver cavity. Normally, solar radiation is focused through an aperture or apertures in the cavity onto the heat exchanger. The heat exchanger, in general, channels the working fluid, and in one embodiment may consist of a honeycomb of tubes. These tubes are oriented so that focused solar energy impinging on the honeycomb travels down the tubes where it is absorbed. For convenience, the illuminated end of the heat exchanger is called its "face". While the subject invention applies to a number of different solar energy receivers, it will be described in connection with this type solar energy receiver for convenience.
Solar energy receivers have been mounted on masts or in so-called "power towers" above a mirror field which redirects solar energy and focuses it onto the receiver. As a result of the use of as many as 1,000 mirrors, concentrated solar energy may cause the solar receiver to exceed temperatures of 3,000.degree. F. In order to withstand the intense solar radiation, heat exchangers of exotic materials such as silicon carbide or ceramicmetal composites have been used, with the heat exchanger materials being chosen to withstand the high input temperatures. The high input temperatures were thought necessary to insure that high exit gas temperatures could be efficiently achieved. However, at these high temperatures, and more particularly, for sharp, non-linear temperature profiles aklong the heat exchanger, tremendous thermal stress is introduced which causes distortion of the heat exchanger. While solar energy receivers of the type described work reasonable satisfactorily, unless heat exchanger tubes are made from exotic costly materials, the tubes may buckle, and tend to turn inside out under this type stress. This limits the useful life of the heat exchanger for some commercial applications. For commercially acceptable power production applications, major equipment lifetimes in excess of 30 years are required. Thus, for high temperature solar receivers to be commercially acceptable, either very costly heat exchanger materials must be used or some method must be provided to insure long life with more conventional materials.
More particularly, most common materials degrade significantly at temperatures above 3,000.degree. F. and their use in "power tower" applications presents serious problems. The degradation of materials which occurs at high temperatures refers to mechanical failures in which the heat exchangers crack or melt, and to factors which reduce heat transfer from the walls of the heat exchanger to the working gas, such as corrosion, errosion, or chemical change.
With oxidation at high temperatures, heat exchanger materials become weakened and crack. Moreover, at high temperatures, the phenomenon of "creep" exists, in which upon heating the thermal expansion is so great that the heat exchanger materials distort and become weakened. "Creep" implies non-elastic deflections so that a relatively small, but steady force produces a growing deflection. Of course, at temperatures above 3,000.degree. F., there is a possibility of the melting of the heat exchanger material or bringing the material close to the melting point, which also results in a weakening of the structure and potential physical failure.
In addition to the effect of thermal shock on the materials in terms of physical failure, there may be a change in the emissivity of the walls of the heat exchanger due to chemical degradation or errosion which lowers receiver efficiency. In addition, the efficiency of the receiver can be further affected through surface degradation by reductions in the "h" or "U.sub.eff " value, where "h" is the "film coefficient of heat transfer" at a point and "U.sub.eff " is an averaged value over the internal heat exchanger area. "h" is generally a local microscopic coefficient which may vary from place to place, while "U.sub.eff " is generally an overall averaged value of heat transfer coefficient.
It is a finding of the subject invention that with a unique selection of the solar receiver convective index and flow index, efficiencies exceeding 85% may be obtained with output temperatures of 1800.degree. - 2000.degree. F., in which the working temperature of the heat exchanger is substantially uniform throughout its length and need never exceed the 2000.degree. F. outlet air temperature by more than 100.degree. F. That is to say, it is now possible to efficiently obtain sufficiently high exit gas temperatures without the necessity of heating any part of the heat exchanger substantially above the outlet air-temperature. Moreover, with a uniform heat distribution, thermally induced stress on the heat exchanger is significantly reduced which results in prolonged life for the heat exchanger. Additionally, because of the lowered operating temperature the corrosion and oxidation aspect associated with solar energy receivers is greatly reduced. Also, with reduced input temperatures thermal reradiation is reduced (T.sup.4 law) which materially aids conversion efficiency. It should be noted that exit gas temperatures of 1800.degree. F. or greater are clearly sufficient for the utilization of the subject solar energy receiver in a so-called Brayton cycle engine type power plant. Moreover, lower exit gas temperatures are useful when the gas is utilized to form steam in a conventional boiler type application.
In order to obtain the above noted efficiencies while running the receiver at no greater than 2000.degree. F., perhaps the most important set of parameters are the Graetz number, N.sub.Gr, the flow index, I.sub.FLOW, and the convective index, I.sub.c, of the receiver, all defined hereinafter. It is a finding of the subject invention that the flow index, when set such that the Graetz number is approximately equal to 6, provides optimal heat transfer without excessive pumping energy. Once the flow index has been set, it is then desireable to set the convective index of the solar receiver to be two times the flow index. This provides the optimal balance between heat transfer efficiency and receiver size, such that if the convective index is less than two times the flow index, efficiency is lost; whereas building a receiver where the convective index is much greater than two times the flow index, merely results in greater receiver size without any corresponding advantage. What is achieved is a receiver size which is set exactly at the point of optimal performance and useful life expectancy, thereby to eliminate excess size and cost.
As a matter of practically achievable tolerances, as well as impact on the efficiency, both the Graetz number and the flow index should not exceed the nominal values stated here, but may be as far as a factor of 2 below these levels before the impact on efficiency exceeds 10-20% of the optimal efficiency. For the convective index, the tolerances are stated differently. The nominal value may be exceeded by any amount desired, but any excess represents higher cost for negligible returns (gain in performance). On the downside I.sub.c may go as far as half the nominal value to degrade the projected efficiency from 88% to 82%. It should be emphasized that a solar receiver will "work" over a broad range about the nominal values, but will work best when "tuned" to the recommended levels. In practice, one might modify the receiver aperture and/or the flow rate in the field, as allowed by turbine considerations or by the solar flux pattern to optimize overall efficiency.
In order to set the flow index such that the Graetz number is equal to 6 various other parameters become important. First, the flow index must be set less than, but as close as practical to 6kL/D.sup.2 r.sub.c such that the aforementioned Graetz number will not exceed, but will approximately equal 6, within reasonable design tolerance. Here k is the thermal conductivity of the gas, L is the length of the heat exchanger tube, D is its diameter, and r.sub.c is the cavity ratio of the receiver, e.g. r.sub.c = area of the illuminated face of the heat exchanger, A.sub.h, divided by the area of the receiver aperture, A.sub.Ap. This also takes into account the sublaminar flow conditions that exist in any efficient solar receiver. Obviously, there is a balance between turbulent flow which is more effective for heat transfer than laminar flow, and laminar flow which utilizes less pumping energy. Note, the object is to avoid turbulence because turbulence always causes heavy increases in energy required to maintain fluid flow. N.sub.Gr as large as possible short of 6 leads to maximum possible heat transfer short of requiring heavy expenditure of mechanical energy to maintain circulation.
For the convective index to be two times the flow index, I.sub.c is defined as hA.sub.s /A.sub.Ap, or more generally U.sub.eff A.sub.s /A.sub.Ap, which the designer sets as closely as practical to the target value of twice the flow index. Here A.sub.s is the internal heat exchanger area exposed to solar radiation.
In order to achieve the Graetz number approximately equal to 6 along with the corresponding condition for flow index, it is practical to have the cavity ratio, r.sub.c, greater than one. Moreover, the optical index in one operative embodiment is set greater than 6 in order to achieve maximum efficiency.
When all of the parameters just described are appropriately set, it is a unique finding of this invention that as solar energy is transferred to the heat exchanger the heat exchanger quickly achieves a relatively uniform temperature not exceeding 2000.degree. F. throughout its length, thereby permitting the utilization of less expensive, less exotic heat exchanger materials and construction methods. Moreover, the heat exchanger is designed to a length which insures that the gas through the receiver attains the desired exit temperature at exactly the exit end of the heat exchanger, so that no excess heat exchanger material is used.
What has been found, is that it is not necessary to excessively heat up the face of the heat exchanger exposed to the focused radiation in order to obtain desired output temperatures. More generally, it has been found that it is possible with proper design to keep the temperature profile of the heat exchanger relatively flat, thereby to be able to lower the input temperature close to the chosen output temperature without losing efficiency. This means that fewer mirrors need be used which results in substantial cost savings. In addition to significantly reducing thermal shock, the lower input temperature permits running of the receiver at a minimum input temperature for a given or desired output temperature. As a result the requirements for the heat exchanger material are minimized. Most importantly, there is a striking gain in efficiency by reducing the T.sup.4 reradiation with lower working temperatures.
This finding, predicated upon the above mentioned parameters, determines the appropriate size of the face of the heat exchanger, its spacing from the aperture of the solar energy receiver, the mass flow rate through the receiver and other critical parameters which insure an extremely high efficiency, low cost, long life solar energy receiver. If the suggested parameters are exceeded in any one direction, either efficiency will be lost or the amount of material for making the solar energy receiver increases substantially thereby increasing the cost of the solar energy receiver without increased efficiency.
It is therefore an object of this invention to provide a solar energy receiver with an improved useful life.
It is another object of this invention to provide a method of setting the parameters of a solar energy receiver which utilizes fluid heated by focused solar radiation.
It is a still further object of this invention to provide a solar energy receiver in which the efficiency is maximized while at the same time running the solar receiver at minimum input temperatures.
It is a still further object of this invention to provide solar energy receivers in which the danger of thermal/mechanical failure is minimized, and in which the mean time to failure is lengthened. These and other objects of the invention will be better understood in connection with the following description in view of the appended drawings in which: